Details

Time bar (total: 9.8s)

sample34.0ms

Algorithm
intervals
Results
10.0ms281×body80valid
4.0ms120×body80nan

simplify67.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01214
12214
24614
37214
49714
511214
done11214

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
4.6b
(* (* x y) z)
7.8b
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.9b
(sqrt (- (* z z) (* t a)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
11×add-sqr-sqrt
10×pow1 add-cube-cbrt *-un-lft-identity
9×sqrt-prod
6×times-frac prod-exp associate-/r* cbrt-unprod add-log-exp
4×expm1-log1p-u sqrt-div log1p-expm1-u
3×cbrt-undiv flip3-- div-exp associate-*r* pow-prod-down flip--
2×associate-/r/
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log associate-*l* prod-diff clear-num *-commutative div-inv associate-/l*
Counts
4 → 86
Calls
4 calls:
10.0ms
(- (* z z) (* t a))
17.0ms
(* (* x y) z)
29.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
13.0ms
(sqrt (- (* z z) (* t a)))

series221.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(- (* z z) (* t a))
25.0ms
(* (* x y) z)
94.0ms
(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
64.0ms
(sqrt (- (* z z) (* t a)))

simplify1.0s

Counts
98 → 98
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01461331
13611220
215601062
done50011060

prune287.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* z z) (* t a))) z)
0.6b
(- (* z z) (* t a))
4.2b
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
23.9b
(sqrt (- (* z z) (* t a)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
47×add-sqr-sqrt
46×add-cube-cbrt *-un-lft-identity
33×sqrt-prod
25×associate-/r*
18×add-exp-log add-cbrt-cube
7×cbrt-undiv div-exp associate-/l*
6×add-log-exp
5×pow1
4×expm1-log1p-u sqrt-div log1p-expm1-u div-inv
3×flip3-- flip--
2×frac-2neg prod-exp clear-num cbrt-unprod associate-/l/
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log prod-diff associate-/r/
Counts
4 → 142
Calls
4 calls:
20.0ms
(/ (sqrt (- (* z z) (* t a))) z)
9.0ms
(- (* z z) (* t a))
20.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
11.0ms
(sqrt (- (* z z) (* t a)))

series265.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(/ (sqrt (- (* z z) (* t a))) z)
38.0ms
(- (* z z) (* t a))
93.0ms
(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
62.0ms
(sqrt (- (* z z) (* t a)))

simplify1.1s

Counts
154 → 154
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02222758
15222513
216932314
done50012309

prune412.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt z)
1.9b
(* (/ x (/ (sqrt (sqrt (- (* z z) (* t a)))) (* (cbrt z) (cbrt z)))) (/ y (/ (sqrt (sqrt (- (* z z) (* t a)))) (cbrt z))))
23.9b
(sqrt (- (* z z) (* t a)))
23.9b
(sqrt (- (* z z) (* t a)))

rewrite274.0ms

Algorithm
rewrite-expression-head
Rules
523×times-frac
382×add-sqr-sqrt
249×sqrt-prod
203×add-cube-cbrt *-un-lft-identity
179×associate-*r*
99×cbrt-prod
58×add-exp-log
48×add-cbrt-cube
44×associate-*l*
40×unswap-sqr
27×cbrt-undiv div-exp
15×prod-exp cbrt-unprod
8×pow1 div-inv
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
2×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 associate-/r/ flip--
1×frac-times pow1/3 associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 348
Calls
4 calls:
1.0ms
(cbrt z)
220.0ms
(* (/ x (/ (sqrt (sqrt (- (* z z) (* t a)))) (* (cbrt z) (cbrt z)))) (/ y (/ (sqrt (sqrt (- (* z z) (* t a)))) (cbrt z))))
11.0ms
(sqrt (- (* z z) (* t a)))
14.0ms
(sqrt (- (* z z) (* t a)))

series422.0ms

Counts
4 → 12
Calls
4 calls:
174.0ms
(cbrt z)
115.0ms
(* (/ x (/ (sqrt (sqrt (- (* z z) (* t a)))) (* (cbrt z) (cbrt z)))) (/ y (/ (sqrt (sqrt (- (* z z) (* t a)))) (cbrt z))))
65.0ms
(sqrt (- (* z z) (* t a)))
68.0ms
(sqrt (- (* z z) (* t a)))

simplify856.0ms

Counts
360 → 360
Iterations

Useful iterations: done (842.0ms)

IterNodesCost
058213298
1185012316
done500011485

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* z z) (* t a))
1.0b
(/ y (/ (sqrt (- (* z z) (* t a))) z))
2.0b
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
23.9b
(sqrt (- (* z z) (* t a)))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
263×times-frac
157×add-sqr-sqrt
143×add-cube-cbrt *-un-lft-identity
71×associate-*r*
67×sqrt-prod
22×associate-/r*
18×add-exp-log add-cbrt-cube
9×div-inv
7×pow1
6×cbrt-undiv div-exp add-log-exp
4×expm1-log1p-u log1p-expm1-u unswap-sqr
3×associate-*l* prod-exp cbrt-unprod associate-/l*
2×flip3-- sqrt-div associate-/r/ flip--
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log associate-*r/ prod-diff pow-prod-down clear-num *-commutative
Counts
4 → 237
Calls
4 calls:
9.0ms
(- (* z z) (* t a))
16.0ms
(/ y (/ (sqrt (- (* z z) (* t a))) z))
52.0ms
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
11.0ms
(sqrt (- (* z z) (* t a)))

series266.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(- (* z z) (* t a))
61.0ms
(/ y (/ (sqrt (- (* z z) (* t a))) z))
97.0ms
(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
68.0ms
(sqrt (- (* z z) (* t a)))

simplify1.3s

Counts
249 → 249
Iterations

Useful iterations: done (1.3s)

IterNodesCost
03424983
18024462
223414239
done50014235

prune632.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.2b

regimes322.0ms

Accuracy

84.6% (3.0b remaining)

Error of 6.4b against oracle of 3.4b and baseline of 22.7b

bsearch93.0ms

Steps
ItersRangePoint
9
3.897635107664822e+95
3.2935197406763337e+100
3.938152743281577e+96
9
-6.208254577570641e+60
-2.497316010543444e+54
-1.0028371986688996e+60

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02647
13147
23447
done3447

end0.0ms

sample931.0ms

Algorithm
intervals
Results
321.0ms8879×body80valid
94.0ms2977×body80nan